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Culture War Roundup for the week of December 11, 2023

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Sounds right to me.

Do you think we can rigorously define the Kolmogorov complexity of the Christian God, and/or infinite looping universes based on unknown physics?

So there's the trivial answer, which is that the program "run every program of length 1 for 1 step, then every program of length 2 for 1 step, then every program of length 1 again, and so on [1,2,1,3,1,2,1,4,1,2,...] style" will, given an infinite number of steps, run every program of finite length for an infinite number of steps. And my understanding is that the Kolmogorov complexity of that program is pretty low, as these things go.

But even if we assume that our universe is computable, you're not going to have a lot of luck locating our universe in that system.

Out of curiosity, why do you want to know? Kolmogorov complexity is a fun idea, but my general train of thought is that it's not avtually useful for almost anything practical, because when it comes to reasoning about behaviors that generalize to all turing machines, you're going to find that your approaches fail once the TMs you're dealing with have a large number (like 7 for example, and even 6 is pushing it) of states.

We're debating epistemology, and @self_made_human is arguing that some unfalsifiable theories about the origin of the universe are superior to others because they are "lower complexity" in the information-theory sense, which he proposed measuring through Kolmogorov complexity. My position is that there is no way to rigorously measure the Kolmogorov complexity of the Christian God, or of the Karmic Wheel, or of a universe that loops infinitely via unknown physics even in principle; you cannot measure things you cannot adequately describe, and mechanisms that are unobservable and unfalsifiable cannot be adequately described by definition.

It is not just that they are lower complexity, it's that for a given amount of evidence, Bayesian reasoning privileges simpler answers. If additional complexity helps predict the behavior of system better, then we accept it. F=ma is far simpler than General Relativity or QM, but the latter generalize to situations where Classical Mechanics fails.

PDF warning:

Bayesian Occam’s Razor Is a Razor of the People

Abstract

Occam’s razor—the idea that all else being equal, we should pick the simpler hypothesis— plays a prominent role in ordinary and scientific inference. But why are simpler hypotheses better? One attractive hypothesis known as Bayesian Occam’s razor (BOR) is that more complex hypotheses tend to be more flexible—they can accommodate a wider range of possible data—and that flexibility is automatically penalized by Bayesian inference. In two experiments, we provide evidence that people’s intuitive probabilistic and explanatory judgments follow the prescriptions of BOR. In particular, people’s judgments are consistent with the two most distinctive characteristics of BOR: They penalize hypotheses as a function not only of their numbers of free parameters but also as a function of the size of the parameter space, and they penalize those hypotheses even when their parameters can be “tuned” to fit the data better than comparatively simpler hypotheses.

Abrahamic God, the Standard Model etc all claim to explain the world as we observe it.

The former is absolutely rubbish at predicting future events, and to the extent that you are under the impression that God is responsible for ensuring the operation of the Standard Model (or a complete description of physics), it is necessarily more complex.

Since belief in God does nothing to constrain future expectations be it for novel evidence or even developing practical models for simulating things, it is largely worthless, and unless you start from the assumption, no rational agent will reach it.

In this context, Kolmogorov complexity is one way of representing the notion that certain ideas or hypotheses that seem intuitively "simple" are not actually so in any more rigorous sense.

It is not just that they are lower complexity, it's that for a given amount of evidence, Bayesian reasoning privileges simpler answers.

Yes. But when the "given" amount of evidence is "Zero" for multiple answers, BOR has no method to distinguish between them.

Is [unknown number of digits excluded]12084038 bigger or smaller than [unknown number of digits excluded]0? The answer is mu, because we don't have the necessary data to do the math. You have claimed that we can do math with no data whatsoever. In the first place, this claim seems clearly wrong, but in the second place, it seems very interesting that someone as intelligent as you would make it.

There is no available evidence about what caused the Big Bang at all, and there is no rigorous definition of "simpler" by which any speculations we may have might be measured.

We agree that effects have causes within our system. We agree (I think) that there is an effect whose causes are unobservable from within our system, at least given our current understanding. Since effects have causes, and since we cannot observe a cause for this effect from within our system, the cause must come from outside our system. Since we cannot see outside our system, we have zero evidence about the nature of that cause. Since we have zero evidence, tools like BOR and Kolmogorov Complexity cannot be used to select theories in a rigorous fashion.

Abrahamic God, the Standard Model etc all claim to explain the world as we observe it. The former is absolutely rubbish at predicting future events,

Abrahamic God and the Standard Model are not necessarily competing explanations for the world we observe.

...and to the extent that you are under the impression that God is responsible for ensuring the operation of the Standard Model (or a complete description of physics), it is necessarily more complex.

It is indeed necessarily more complex than the Standard Model. In exactly the same way, "True Physics" being responsible for ensuring the operation of the Standard Model is necessarily more complex than the standard model.

Given that we have to add something, and given that we have zero data from the hard sciences on what that something is, we likewise have no concrete evidence of which explanation is more or less complex than another.

In this context, Kolmogorov complexity is one way of representing the notion that certain ideas or hypotheses that seem intuitively "simple" are not actually so in any more rigorous sense.

Certainly. But you are the one claiming that some unobservable hypotheses or ideas are simpler than others, and it seems you cannot actually use Kolmogorov Complexity to prove it in the way you claimed you could.

I reiterate that I am not attempting to convince you to believe in the Christian God. I am trying to demonstrate an observable, verifiable, testable fact: that all beliefs are chosen. It seems to me that you are appealing to Kolmogorov Complexity and Bayesian Occam's Razor because you want to claim that your commitment to materialism is not a choice, but rather a deterministic outcome of accumulated evidence. But it seems obvious to me that neither KC nor BOR can possibly work the way you are trying to use them, and in fact neither is the source of your conviction.

You called for an expert, and it seems to me that the expert flatly contradicted your claims. Does the reversal of expected evidence change your position any? If not, what evidence does your conviction derive from?

BOR does have implications for when we have zero evidence.

And that would be to choose the most minimal potential hypothesis, though I am unsure what that could possibly mean. What hypothesis explains a coin flip that never happened?

It is, however not true that we have "zero" evidence about what caused the Big Bang. After all, I presume you admit that there could be evidence along the lines of say, the cosmic microwave background radiation spelling out "God here. Glad you're reading this, good to see you're advancing up the tech tree" in English, and you (and I) would have no qualms about ascribing that as evidence for God causing the Big Bang? I don't think either of us would claim that it has no relevance, that it cannot be the case that observations made within a universe could inform our understanding of what lies outside it.

In a similar vein, to the extent that you expect a universe designed by the Judeo Christian deity to differ in any way from one that's purely mechanistic, the absence of such evidence is Bayesian evidence of absence.

It is indeed necessarily more complex than the Standard Model. In exactly the same way, "True Physics" being responsible for ensuring the operation of the Standard Model is necessarily more complex than the standard model.

It may be more complex. It is not necessarily so. Much of the charm of the Standard Model is that by establishing symmetries, it simplifies and explains whole bunch of seemingly disparate observations. You can imagine someone who studiously makes a table showing the rates of deceleration for a whole range of different masses under gravity, which is actually useful in real life, but more complex when compared to just applying Newtonian gravity and air resistance when supplied with a given value for m. I am mostly agnostic on whether the GUT will be "simpler" than the Standard Model, even if I'm mildly expecting that to be the case. Physicists certainly consider it desirable, but the only true necessity is that it explains things better, especially for situations not in the data used to derive it.

Certainly. But you are the one claiming that some unobservable hypotheses or ideas are simpler than others, and it seems you cannot actually use Kolmogorov Complexity to prove it in the way you claimed you could.

Kolmogorov complexity is a beast, but if you really cared to, you could easily substitute minimum message length or Shannon entropy and get the same result.

In fact, it was an error (or at least suboptimal) for me to even bring up KC, when MML exists:

https://en.wikipedia.org/wiki/Minimum_message_length

Minimum message length (MML) is a Bayesian information-theoretic method for statistical model comparison and selection.[1] It provides a formal information theory restatement of Occam's Razor: even when models are equal in their measure of fit-accuracy to the observed data, the one generating the most concise explanation of data is more likely to be correct (where the explanation consists of the statement of the model, followed by the lossless encoding of the data using the stated model). MML was invented by Chris Wallace, first appearing in the seminal paper "An information measure for classification".[2] MML is intended not just as a theoretical construct, but as a technique that may be deployed in practice. [3] It differs from the related concept of Kolmogorov complexity in that it does not require use of a Turing-complete language to model data.[4]

Besides, it's not just the Big Bang we're considering, it's the Big Bang and everything else. Here, once again, BOR implies that God is a terrible answer.

I apologize for the digression into KC, even if that's an interesting topic.

I reiterate that I am not attempting to convince you to believe in the Christian God. I am trying to demonstrate an observable, verifiable, testable fact: that all beliefs are chosen. It seems to me that you are appealing to Kolmogorov Complexity and Bayesian Occam's Razor because you want to claim that your commitment to materialism is not a choice, but rather a deterministic outcome of accumulated evidence. But it seems obvious to me that neither KC nor BOR can possibly work the way you are trying to use them, and in fact neither is the source of your conviction.

All beliefs are not a choice, assuming you're using "choice" in the standard sense.

A person suffering from Capgras delusion, who believes that his kin have been replaced by body snatchers, is not choosing to think so. You can argue with him, shake him about, shock him with a cattle prod, and he will never relent. The disease has stolen away even the option for him to think otherwise. A schizophrenic does not "choose" to think he's the reincarnation of Jesus or Napoleon.

You called for an expert, and it seems to me that the expert agreed with me that KC can't do what you claimed it did. Does the reversal of expected evidence change your position any? If not, what evidence does your conviction derive from?

I am pretty sure that @faul_sname agrees with my statements regarding the "objective" Kolmogorov complexity of different hypothesis. I know, and he knows I know that it's incomputable, because that came up as the subject of conversation not that long ago. But while Kolmogorov complexity might not be an ideal use case for anything except theoretical discussions, MML is, and I should have substituted it at the start if I remembered that the latter is a practical metric.

In this case, the relevant update for me is to do a better job of representing theories I only understand at a superficial level, not a knock against the generalized claim I'm making.

I suspect that "belief", rather than "choice", is the word that you two are using differently. You can't choose your "beliefs(1)" in the sense of "what you anticipate what your future experiences will be contingent on taking some specific course of action", but you can choose your "beliefs(2)" in the sense of "which operating hypothesis you use to determine your actions".

I might be wrong though. It is conceivable to me that some people can change their beliefs(1) by sheer force of will.

English, a language stunningly unsuitable for such discussions, not that I know of one that's better.

I might be wrong though. It is conceivable to me that some people can change their beliefs(1) by sheer force of will.

@FCfromSSC claims to be able to do this, including intentionally convincing himself that a chair he's sitting on is a fake. I'm capable of no analogous feat, but it's hardly the weirdest thing that human cognition has done, and I'll accept his word for it.

I have not ever convinced myself of the nonexistence of a chair I was sitting on.

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